We computationally investigate the unsteady pulsatile propagation of a finger of air through a liquid-filled cylindrical rigid tube. The flow field is governed by the unsteady capillary number Ca_Q(t)=μQ (t )/πR~2γ, where R is the tube radius, Q is the dimensional flow rate, t is the dimensional time, μ is the viscosity, and γ is the surface tension. Pulsatility is imposed by Ca_Q(t ) consisting of both mean (Ca_M) and oscillatory (Ca_Ω components such that Ca_Q(t)=Ca_M + Ca_Ω sin(Ωt). Dimensionless frequency and amplitude parameters are defined, respectively, as Ω =μωR/γ and A=2CaΩ/Ω, with ω epresenting the frequency of oscillation. The system is accurately described by steady-state behaviour if CaΩ Ca_M, reverse flow exists during a portion of the cycle, leading to an unsteady regime. In this unsteady regime, converging and diverging surface stagnation points translate dynamically along the interface throughout the cycle and may temporarily separate to create internal stagnation points at high Ω. For Ca_Ω <10Ca_M, the bubble tip pressure drop △P(tip) may be estimated accurately from the pressure measured downstream of the bubble tip when corrections for the downstream viscous component of the pressure drop are applied. The normal stress gradient at the tube wall θτ_n/θz is examined in detail, because this has been shown to be the primary factor responsible for mechanical damage to epithelial cells during pulmonary airway reopening (Bilek, Dee & Gaver III 2003; Kay et al. 2004). In the unsteady regime, local film-thinning produces highθ τ_n/θz at low Ca_Ω; however, film thickening at moderate Ca protects the tube wall from large θτ_n/θ_z. This stress field is highly dynamic and exhibits intriguing spatial and temporal characteristics that may be used to reduce ventilator-induced lung injury.
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